IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-11795-4_71.html

Adaptive SQP Method for Shape Optimization

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • P. Morin

    (Universidad Nacional del Litoral, CONICET, Instituto de Matemática Aplicada del Litoral)

  • R. H. Nochetto

    (University of Maryland, Department of Mathematics and Institute for Physical Science and Technology)

  • M. S. Pauletti

    (University of Maryland, Department of Mathematics
    Department of Mathematics)

  • M. Verani

    (Politecnico di Milano, MOX – Dipartimento di Matematica “F. Brioschi”)

Abstract

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state equation, update the boundary, and compute the geometric functional. We present a novel algorithm that uses a dynamic tolerance and equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution – a new paradigm in adaptivity.

Suggested Citation

  • P. Morin & R. H. Nochetto & M. S. Pauletti & M. Verani, 2010. "Adaptive SQP Method for Shape Optimization," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 663-673, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_71
    DOI: 10.1007/978-3-642-11795-4_71
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-11795-4_71. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.